One great thing about Manchester is that you can walk from one end of the city centre to the other in about 40 minutes or so, there are lots of museums and shops to see in between, and one of those city centre ferris wheels.
I recommend the Museum of Science & Industry, but imo its a bit geared towards kids, there is a cathedral which is lovely, the City Art Gallery, China Town, Canal Street, unfortunately Urbis is closed, but that was interesting also. The Lowry in Salford is very interesting, as is the Imperial War Museum North. You can head out of town for a curry in Rusholme, and go to the Costume Gallery at Platt Fields, also Whitworth Art Gallery is great. If you are interested in the Smiths at all, you can follow the lyrics of some of their songs and visit the Cemetery Gates at Southern Cemetery, See the Salford Lads Club, go to his childhood house on Kings Road (right around the corner from my house!!!) There is great shopping in Manc, great food, great people....Enjoy the city! Its a brilliant place to be!!
(do I sound like the mayor??)